Balanced Group Maker

Describe what the user wants in plain words and get back whether this server can do it, which limits it would hit, and the closest thing it CAN do. Instant, no solve. Use it when unsure the tool fits (seating charts, tournament brackets, round-robin schedules, random draws, repeated rotations, very large lists).

Return the full input JSON of one example, in exactly the shape make_groups accepts: 'classroom' = 30 students, 6 groups, together and apart codes, categorical and numeric fields, blanks; 'teams' = 20 colleagues in 4 teams balanced on a numeric skill and a role. Edit it (people, fields, priorities, number of groups) to match the user's situation.

Fetch the result of a make_groups job that returned status 'running'. Waits up to wait_seconds; call again while status is 'running'. Jobs expire 15 minutes after they finish.

Split people into balanced groups with a MILP solver and return each group's members, a per-group summary of every field, the overall mix, a balance score per field (100 = perfectly balanced), notes and warnings. Give `groups` (a number of groups; sizes then differ by at most 1) OR `min_size` and/or `max_size` (the server tries every group count that fits and picks the best); with both, `groups` decides and the sizes only validate it. `priorities` maps a field to 1 (most important), 2, 3...; a field left out counts least; equal numbers tie. Solves take up to about 20 s. If the result has status 'running', call get_group_result with its job_id. If it has status 'busy', wait the retry_after_seconds it gives and call again -- one call at a time, never in parallel. If it has status 'error' or 'infeasible', the message says in plain words what to change. Defaults applied (e.g. a field with no priority) are listed in `assumptions`; tell the user about them. Call get_group_example for a complete, realistic input.